Few-Shot Diffusion Models Escape the Curse of Dimensionality

While diffusion models have demonstrated impressive performance, there is a growing need for generating samples tailored to specific user-defined concepts. The customized requirements promote the development of few-shot diffusion models, which use limited n_{ta} target samples to fine-tune a pre-trained diffusion model trained on n_s source samples. Moreover, the existing results for diffusion models without a fine-tuning phase can not explain why few-shot models generate great samples due to the curse of dimensionality. In this work, we analyze few-shot diffusion models under a linear structure distribution with a latent dimension d . From the optimization perspective, we consider a latent Gaussian special case and prove that the optimization problem has a closed-form minimizer.